Practical answer
What about work email?
For most jobs, email at a desk is a feature rather than a limitation. For some jobs it genuinely isn't.
Be honest about which of these describes your work.
Email can wait
Most office and professional roles do not require email within minutes. Checking at a desk three or four times a day is normal and was normal recently. Tell colleagues to call you for anything urgent — the simple phone handles calls perfectly.
Email genuinely cannot wait
If you are on call, run a business where deals move hourly, or manage emergencies, you need a device with email. That points toward an Essential Apps Phone or a Filtered Smartphone rather than a flip phone.